SFB 303 Discussion Paper No. B - 160

Author: Kottmann, Thomas, and Irene Kuliberda
Title: Autoregressive Models with Forecast Feedback: A Monte-Carlo-Study and First Theoretical Results
Abstract: During the last five years there has been considerable progress in the analysis of learning procedures towards rational expectations. The results can be roughly summarized as follows: Under kind-of ergodicity assumptions ordinary-least-squares-type learning procedures converge to generalized rational expectations if the influence of the forecast terms is not too large (Kottmann (1990a), (1990b)).The most serious deficiency of these results is that they do not apply right off to models with lagged endogenous variables. The reason is that models with forecast feedback and lagged endogenous variables exhibit extraordinarily complicated dynamics.The lack of satisfactory theoretical results gave rise to the Monte-Carlo-study that is to be reported here. For a simple autoregressive forecast feedback model with three numerical parameters standard OLS-learning has been simulated. It turned out that these simulations exhibit a behaviour considerably different from the theoretical results for models without lagged endogenous variables.Motivated and guided by the simulation results, for models with forecasts of the current endogenous variable a theoretical proof of convergence has been derived. It is given in section 4, makes use of martingale convergence arguments and may be accessible to generalization to models with forecasts of future values. The direction of how this generalization can possibly be achieved is indicated.As to models with forecasts of future values, only heuristical arguments are given. It is supposed, however, that they can be strengthened to formal proofs without much trouble.
Creation-Date: September 1990
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